According to reports in the UK, Kewell, 38, is the hot favourite to replace the sacked Dermot Drummy and the Aussie is expected to be unveiled as early as next week.
It would signal Kewell's first senior managerial position, after leaving his role as Watford Under-23 coach last month.
Crawley Town finished 19th on the 24-team League Two ladder in 2016-17 - just five points clear of the relegation zone and only winning one of their last 14 games.
Kewell, who played for the Socceroos at the 2006 and 2010 FIFA World Cups, said in December that his ultimate goal was to be manager of his former club Liverpool.
"My ultimate goal is Liverpool ... You don't know unless you get thrown in there. I'm a big believer in sink or swim," Kewell said.
Kewell was also recently linked to the Newcastle Jets job, which was eventually filled by Ernie Merrick.
The news of Kewell's imminent arrival hasn't gone down well with some supporters though, who took to Twitter to vent their discontent.
